Abstract
This column is devoted to maximum (respectively, maximum weight) independent set problems in geometric intersection graphs. We illustrate with one example in each class: (I) The following question was asked by T. Rado in 1928: What is the largest number c such that, for any finite set F of axis-parallel squares in the plane, there exists an independent subset I ⊆ F of pairwise disjoint squares with total area at least c times the union area of the squares. (II) The following question was asked by Erdös in 1983: What is the largest number H = H ( n ) with the property that every set of n non-overlapping unit disks in the plane has an independent subset with at least H members?
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